why in algebra class they teach the order of operations (PEMDAS) in that order. Is this just an arbitrary standard everyone agreed on or was it the result of higher math only making sense when equations are done in that order?

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Answer 1

Its just an agreed upon standard. Back in the day mathematicians used to just list out whatever the order of operations they used so the math would be consistent. At some point we agreed this is sort of stupid and academia just standardized it.